After having engine replaced my transmission stopped working

I had to replace the engine, I took my car to the shop. They replaced my engine, then I picked my car up and drove home and parked it. Next morning I started my car let it warm up and put to reverse and transmission would not react. Tried to put to drive still would not react. When I took my car back to shop they start saying that my car is too old I need to replace transmission. When I took to Mazda dealership they told me that they checked code and there is not any codes popped up. They sad there is no pressure in transmission and suggest me to replace transmission. Then I decide to take my car to one more shop they told me there is problem with converter. My transmission works like a brand new. Please help me with your advice what would cause such a problem? Any ideas, what can be wrong?